Measurement-based topological quantum computation using GKP qubits, compatible with a photonic architecture, was considered in Refs. [1]}, [2]}.
The approach was to generate a 3D cluster state to implement a measurement-based analogue of the surface code using GKP qubits.
The cluster state was generated using a post-selection (fusion-based) approach that is non-deterministic by nature.
This work also introduced an analogue quantum-error-correction scheme, where the real-valued measurement outcome from the homodyne measurement was explicitly used in the decoding procedure. The errors considered in Ref. [1]} are finite squeezing effects in the GKP state preparation along with a Gaussian random displacement noise.
More realistic noise, such as loss in the entangling gates and the homodyne measurements, was also considered in Ref. [2]}.
Furthermore, the GKP state preparation is considered to be deterministic and the final state generated is a connected cluster populated only by GKP states.
